Residual Discovery as Open-World Scientific Search: From Anomaly Clusters to Testable Hypotheses Without Reusing Discovery Evidence

Model failure is the engine of scientific progress, but the transition from unexplained observation to testable hypothesis lacks a formal protocol. Posterior predictive checks (Box 1980; Gelman, Meng, and Stern 1996) identify model inadequacy; Bayesian nonparametric methods (Rasmussen 2000; Ferguson 1973) grow hypothesis spaces automatically; preregistration (Chambers 2013; Nosek et al. 2018) constrains post-hoc hypothesis revision and makes it detectable. None of the cited systems supplies the complete typed lifecycle defined here, from residual detection through bin formation, candidate registration, confirmatory evaluation, and versioned disposition. This paper develops a formal methodology for residual discovery as open-world scientific search. The framework begins with observations that are inadequately predicted by all active models. These observations enter an unresolved residual pool rather than being forced into the least-bad available explanation. Residuals may then be grouped into candidate bins according to recurrence, stability, coherence, and novelty. A candidate bin is not yet a hypothesis. It becomes one only when it is compressed into a predictive specification capable of making discriminating claims about unseen data.